A physical limitation of the Wigner "distribution" function in transport

TL;DR

This paper demonstrates that the sign of momentum in the Wigner distribution function does not always indicate the actual direction of particle flow, impacting transport analysis.

Contribution

It reveals a fundamental limitation of the Wigner distribution function's interpretation in transport phenomena, beyond the known uncertainty principle constraints.

Findings

The sign of P in the Wigner function can misrepresent real particle flow direction.

This limitation affects the analysis of electron transport in devices.

The issue is distinct from the traditional uncertainty principle limitations.

Abstract

We present an example revealing that the sign of the "momentum" $P$ of the Wigner "distribution" function $f(q, P)$ is not necessarily associated with the direction of motion in the real world. This aspect, which is not related to the well known limitation of the Wigner function that traces back to the Heisenberg's uncertainty principle, is particularly relevant in transport studies, wherein it is helpful to distinguish between electrons flowing from electrodes into devices and vice versa.